求解5^x=x^5,（5的x次方=x的5次方）,Comparethefunctionsf(x)=x5andg(x)=5xbygraphingbothfunctionsinseveralviewingrectangles.Findallpointsofintersectionofthegraphscorrecttoonedecimalplace.(Enteryouranswersasacomm

Question

求解5^x=x^5,（5的x次方=x的5次方）,
Compare the functions f(x) = x5 and g(x) = 5x
by graphing both functions in several viewing rectangles.Find all
points of intersection of the graphs correct to one decimal place.
(Enter your answers as a comma-separated list.Round any decimal answers
to one decimal place.)
(x,y) = 【 】 (smaller x-value)
(x,y) = 【 】（larger x-value)
Which function grows more rapidly when x is large?
f(x) g(x)

Answer 1

就是求f（x）=5^x-x^5的零点个数
先目测出x=5是一个解
再求证f（x）单调递增 与x轴只有一个交点
那么x=5就是唯一解
不然的话就多解（我自己没证过）